The European Central Bank and the Federal Reserve may soon see policies going in vastly different directions.

Many market participants took ECB President Mario Draghi’s recent speech in Jackson Hole—in which he warned about declining inflation expectations–as a signal that the ECB will embark on a broad-based asset purchase program, known as quantitative easing, in coming months. And most observers expect the Federal Reserve to start raising rates by the middle of next year.

Recent data highlight the diverging paths these economies are taking. U.S. consumer confidence rose to its highest level since 2007 in August. In contrast, a report Wednesday showed German sentiment slipping, and the expectations component plunged by the biggest amount since the survey began in 1980.

But economists differ on whether an extended period of ECB accommodation–beyond the point where the Fed turns policy around–will help the euro zone recover.

“The [policy] divergence will be around for some time,” said Chris Scicluna, an economist with Daiwa Capital Markets. A more accommodative euro-zone policy could weaken the euro, which could help stoke inflation in the euro zone. “A significant weakening of the euro is in order,” said Mr. Scicluna.

A cheaper currency should help euro-zone exporters. It also boosts inflation by making imports more expensive.

The most recent data show annual consumer price inflation in the bloc at 0.4%, a long way off of the ECB’s medium-term target of just below 2%. In contrast, U.S. consumer price inflation is 2%.

A policy difference between the ECB and the Fed isn’t unprecedented. In 2011, the ECB hiked interest rates twice, while the Fed was clearly in an easing mode. The ECB undid those hikes in November and December of the same year and soon thereafter started expanding its balance sheet through three-year loans.

More recently, the ECB’s balance sheet has fallen—by about €1 trillion over the last two years as banks repaid three-year loans early—while the Fed’s has soared due to QE.

The tables may soon turn. The Fed’s balance sheet should stabilize as it concludes its asset purchases, while the ECB is about to offer four-year loans in September, which will cause its balance sheet to increase, as would purchases of asset-backed securities or full-scale QE in Europe.

However, the linkages between the euro zone and the U.S. could make it difficult for the two central banks to run markedly different policies for long.

“Either the global environment gets good enough for the euro-zone outlook to improve–then the ECB will not be on a different path as the Fed for long–or if the global outlook goes down, then the Fed,” would delay a policy tightening, said Berenberg chief economist Holger Schmieding.